The Holborn MP has revealed plans to table amendments to the EU withdrawal bill when it comes to the Commons for its second reading in September.
He said he wanted to “ensure it is possible to achieve transitional arrangements on the same basic terms – including the single market and the customs union”.
A cross-party group of pro-EU Labour and Tory MPs are backing the move, and they believe they may be able to force Prime Minister Theresa May to yield on the issue.
Mrs May is in a precarious position after June’s General Election left her with a minority government propped up Northern Ireland’s DUP.
Theoretically it would only require seven rebel Tory MPs to defeat the bill – and there are a number of Remainer Conservatives sceptical of Brexit and the PM.
If the amendments were passed, it could mean Britain staying tied to Brussels for several years after formally quitting the EU, maintaining the inherent agreements of free trade and movement of people.
But Conservative backbencher Jacob Rees-Mogg told the Sun it was a case of “the metropolitan elite rejecting the result of the Referendum”.
And he accused Mr Starmer of betraying both voters and his own leader Jeremy Corbyn, who has said Britain should leave the single market after Brexit.
“It’s double infamy,” he said.
“He’s betraying the voters – but also his leader, Jeremy Corbyn, who says we will have to leave the single market.”
Dover MP Charlie Elphicke told the Guardian: “There is a clear instruction from the British people to end uncontrolled EU immigration and that means leaving the single market in March 2019.
“It would be wrong for the Labour party to seek to undermine the referendum decision or seek to kick it into the long grass,”
The cross-party group exposes deep divisions in both the Conservative and Labour party’s as Britain ‘s future as a prosperous independent nation hangs in the balance.
Yesterday Mr Rees-Mogg fired a broadside to Tory Remainers by urging them to “stick to the Lancaster House speech”, when the Prime Minister revealed the Government’s position on leaving the single market, customs union, taking control of Britain’s borders and timing over the talks.
Meanwhile, Mr Corbyn is facing pressure from pro-EU Labour moderates to soften his stance over single market access.
The Islington MP has said a Labour government would also leave the single market at the point of Brexit, but would seek a deal similar to the tariff-free benefits enjoyed by EU members.